2.0 Computer Algebra System (CAS) tips
[2.1] Force complete simplification with repeated evaluation
The 89/92+ CAS does not always completely simplify expressions. For example, if you enter this on
the command line
y³|y=2·
√
(2)·r
this is returned
8·2^(3/2)·r³
which is correct but not completely simplified. If you paste this result into the command line and enter it,
the fully simplified result is returned:
1
6*
√
(2)*r³
Another way to force the complete simplificaton seems to be to evalute the expression in a function,
like this:
tt(ex)
func
ex
Endfunc
Executing this call
tt(y^3|y=2·
√
(2)·r)
returns the completely simplified result. Sam Jordan offers these additional comments:
I've noticed the same thing with other large equations. If you enter an expression on the
command line, the TI-89 will automatically simplify it. If it is too complex, it goes as far as
it can, and leave it in a bit simpler state, but doesn't finish it. If you only paste the partially
simplified answer back into the input line, and hit [ENTER] again, it will finish the job. It
seems to set a limit on the amount of work that it does on each pass through the
simplification routine. Eventually you get to the point where re-entering the answer no
longer changes the result, and you can assume that the simplification is complete.
(Credit to Roberto-Perez Franco and Sam Jordan)
[2.2] Try constraints or solve() in symbolic equality tests
With the 89/92+ CAS, you can set two expressions equal to each other, and the CAS can evaluate the
equation and return true or false indicating whether or not the two expressions are equivalent. If the
CAS cannot determine if the two expression are equal, it returns the original equation.
When the CAS fails to resolve the equation to true or false, you can sometimes add domain constraints
to enable the CAS to evaluate the equation. For example, consider
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Summary of Contents for TI-92+
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